Key points are not available for this paper at this time.
Barbero has generalized the Ashtekar canonical transformation to a one-parameter scale transformation U () on the phase space of general relativity. Immirzi has noticed that in loop quantum gravity this transformation alters the spectra of geometrical quantities. We show that U () is a canonical transformation that cannot be implemented unitarily in quantum theory. This implies that there exists a one-parameter quantization ambiguity in quantum gravity, namely, a free parameter that enters the construction of the quantum theory. The purpose of this paper is to elucidate the origin and the role of this free parameter.
Rovelli et al. (Thu,) studied this question.